Author:
Bandyopadhyay S.,Dacorogna B.,Matveev V. S.,Troyanov M.
Abstract
AbstractWe generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0, 2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.
Publisher
Springer Science and Business Media LLC
Reference26 articles.
1. Abraham, R., Marsden, J.E.: Foundations of Mechanics. Second edition, Revised and Enlarged With the Assistance of Tudor Raţiu and Richard Cushman. Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, MA (1978)
2. Ambrose, W., Singer, I.M.: A theorem on holonomy. Trans. Am. Math. Soc. 75, 428–443 (1953)
3. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Translated from the Russian by K. Vogtmann and A. Weinstein. Graduate Texts in Mathematics, vol. 60. Springer-Verlag, New York-Heidelberg, x+462 pp (1978)
4. Bandyopadhyay, S., Dacorogna, B.: On the pullback equation $$\phi ^*(g)=f$$. Ann. Inst. H. Poincaré Anal. Non Linéaire 26(5), 1717–1741 (2009)
5. Bandyopadhyay, S., Dacorogna, B., Kneuss, O.: The pullback equation for degenerate forms. Discrete Contin. Dyn. Syst. 27(2), 657–691 (2010)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献